what is the measure of MNO plz help :))

a. Triangles ABC and DEF are not necessarily congruent.

b. ΔGHI ≅ ΔJKL by the SAS.

c. ΔMNO ≅ ΔPQR by the ASA.

Two triangles are congruent by the ASA congruence theorem if two angles and one included side of one triangle are congruent to two corresponding angles and an included side of the other triangle.

On the other hand, two triangles are congruent by the SAS congruence theorem if two sides and one included angle of one triangle are congruent to two corresponding sides and an included angle of the other triangle.

a. Triangles ABC and DEF only have an indicated pair of congruent angles and a pair of congruent sides which are not enough to prove the triangles congruent.

Therefore, they are not necessarily congruent.

b. The triangles are congruent.

ΔGHI ≅ ΔJKL by the SAS.

c. The triangles are congruent.

ΔMNO ≅ ΔPQR by the ASA.

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Answer:

31

Step-by-step explanation:

hope this helps

The dimensions of the rectangular solid with maximum volume and surface area 13.5 square centimeters are 3 cm by 3 cm by 0.375 cm.

Let's denote the side length of the square base as x, and the height of the rectangular solid as y. Then, the surface area of the rectangular solid can be expressed as:

SA = x^2 + 4xy

And, the volume of the rectangular solid can be expressed as:

V = x^2y

We want to maximize the volume of the rectangular solid subject to the constraint that its surface area is 13.5 square centimeters. This can be expressed as an optimization problem:

Maximize V = x^2y

Subject to SA = x^2 + 4xy = 13.5

We can solve for y in terms of x from the constraint equation:

x^2 + 4xy = 13.5

y = (13.5 - x^2) / 4x

Substituting this expression for y into the formula for V, we get:

V = x^2 (13.5 - x^2) / 4x

V = (13.5 / 4) x^2 - (1 / 4) x^4

To find the maximum volume, we can take the derivative of V with respect to x, and set it equal to zero:

dV/dx = (27/4) x - x^3/4 = 0

27x = x^3

x = 3

So, the maximum volume occurs when x = 3. To find the corresponding height, we can substitute x = 3 into the expression for y:

y = (13.5 - 3^2) / (4 × 3) = 0.375

Therefore, the dimensions of the rectangular solid with maximum volume and surface area 13.5 square centimeters are 3 cm by 3 cm by 0.375 cm.

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The required probability is P(A and B) = 2/36 = 1/18.P(A or B) = P(A) + P(B) - P(A and B) = (1/6) + (1/3) - (1/18) = 5/9

Two events are said to be mutually exclusive if they have no outcomes in common. The sum of probabilities for mutually exclusive events is always equal to 1.

A and B are not mutually exclusive events since the events may occur simultaneously.

The probabilities of A and B are as follows,

P(A) = the probability that they are equal = 6/36 = 1/6 since each number on one dice matches with a particular number on the other dice.

P(B) = the probability that their sum is a multiple of 3.

A sum of 3 and 6 are possible if the 2 numbers that come up on each die are added.

Therefore, the possible ways to obtain a sum of a multiple of 3 are 3 and 6. The following table illustrates the ways in which to obtain a sum of a multiple of 3.  {1,2}, {2,1}, {2,4}, {4,2}, {3,3}, {1,5}, {5,1}, {4,5}, {5,4}, {6,3}, {3,6}, {6,6}

Therefore, P(B) = 12/36 = 1/3 since there are 12 ways to obtain a sum that is a multiple of 3 when 2 number cubes are thrown.

To determine P(A or B), add the probabilities of A and B and subtract the probability of their intersection (A and B).

We can write this as,

P(A or B) = P(A) + P(B) - P(A and B)Let's calculate the probability of A and B,

Both dice must show a 3 since their sum must be a multiple of 3.

Therefore, P(A and B) = 2/36 = 1/18.P(A or B) = P(A) + P(B) - P(A and B) = (1/6) + (1/3) - (1/18) = 5/9

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Answer:

The answer is true

Step-by-step explanation:

To test the hypothesis that population 1 has a mean that is exactly 2 less than the mean of population 2, we can use a two-sample t-test with unequal variances.

The test statistic for this hypothesis is given by:
t = (x1 - x2 - d) / sqrt[(s1^2/n1) + (s2^2/n2)]
where x1 and x2 are the sample means, s1 and s2 are the respective standard deviations, n1 and n2 are the sample sizes, and d is the hypothesized difference in means (in this case, d = 2).
Substituting the given values, we get:
t = (34.5 - 30 - 2) / sqrt[(5^2/33) + (9^2/42)]
t = 2.5 / 1.747
t = 1.43 (rounded to two decimal places)
Therefore, the test statistic for this hypothesis is 1.43.

You want to test the hypothesis that the mean of population 1 is exactly 2 less than the mean of population 2. Given that sample 1 has a mean of 34.5 and sample 2 has a mean of 30, the respective standard deviations are 5 and 9, and the sample sizes are 33 and 42. To find the test statistic, follow these steps:
1. State the null hypothesis (H0) and the alternative hypothesis (H1):
  H0: μ1 - μ2 = 2
  H1: μ1 - μ2 ≠ 2
2. Calculate the difference in sample means (M1 - M2):
  34.5 - 30 = 4.5
3. Calculate the standard error of the difference in means:
  SE = √[(s1²/n1) + (s2²/n2)] = √[(5²/33) + (9²/42)] = √[(25/33) + (81/42)] ≈ 1.595
4. Calculate the test statistic (t):
  t = (M1 - M2 - D) / SE = (4.5 - 2) / 1.595 ≈ 1.568
The test statistic for this hypothesis test is approximately 1.568.

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Answer: 4 pi

Step-by-step explanation:

Answer:

Area = 48π

Step-by-step explanation:

Area of the Sector

\(\text{area of sector} = \pi r^2 \times \frac{\text{angle in degrees}}{360^\circ}\)

r ... radius

Given:

diameter = 24

angle = 120°

Radius is half the diameter.

r = 12

Insert values in the formula.

\(\text{A} = \pi r^2 \times \frac{\text{angle in degrees}}{360^\circ}\)

\(\text{A} = \pi (12)^2 \times \frac{(120)^\circ}{360^\circ}\)

And calculate. But do not multiply with pi. Only multiply numbers.

\(\text{A} = \pi \times 144 \times \frac{1}{3}\)

\(\text{A} = \pi 48\)

\(\text{A} = 48 \pi\)

The beta estimate for the given information with P=10 weeks, O=6 weeks, and M=5 weeks is approximately 8.17 weeks.

In project management, the beta estimate is determined using the Program Evaluation and Review Technique (PERT). It involves taking into account the optimistic time estimate (O), the most likely time estimate (M), and the pessimistic time estimate (P).

To calculate the beta estimate, we use the formula: Beta Estimate = (O + 4M + P) / 6. In this case, the optimistic time estimate is 6 weeks, the most likely time estimate is 5 weeks, and the pessimistic time estimate is 10 weeks. Plugging these values into the formula, we get (6 + 4 * 5 + 10) / 6 = 8.17 weeks (rounded to two decimal places).

Therefore, the beta estimate for the given information is approximately 8.17 weeks.

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the two true statements are the median score for the first 12 games is 19. The range of the first 12 games is 9.

The basketball player scored the following points during the regular season: 15, 16, 17, 18, 19, 20, 20, 22, 24. In the playoffs, the player scored 10 and 45 points.

The median score for the first 12 games is 19.

To find the median, we first need to arrange the scores in order from lowest to highest: 15, 16, 17, 18, 19, 20, 20, 22, 24. The middle score is the median, which in this case is 19.

The range of the first 12 games is 9.

The range is the difference between the highest and lowest scores. The highest score is 24 and the lowest score is 15, so the range is 24 - 15 = 9.

Therefore, the two true statements about the scores for the first 12 games are:

The median score for the first 12 games is 19.

The range of the first 12 games is 9.

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Answer:

it would be 7

Step-by-step explanation:

the equation would be ( if you read the problem) -2+9 and that is equal to 7

The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

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The theorem that can be used to explain each step of the following proof is the basic definition of a circle.The basic definition of a circle states that it is the set of all points in a plane that are equidistant from a given point. If the given point is (h, k), then the circle can be written as (x - h)2 + (y - k)2 = r2. This can be used to explain each step in the proof.

In the given proof, the following reasons can be given for each step:

The axiom of a circle can be used to explain this step. The center and radii of a circle are the defining features of a circle.This step can be explained using the definition of a contradiction.

A contradiction is a statement that goes against a previously proven statement. Therefore, the assumption that 0 = 0 can be proven false by using a contradiction.

: This step can be explained using the proposition that a line can be drawn between any two points. In this case, the two points are O and A.

This step can be explained using the definition of a triangle. A triangle is a polygon with three sides. In this case, the points C, C0, and O are the vertices of the triangle

This step can be explained using the definition of the radius of a circle. The radius of a circle is the distance from the center of the circle to any point on the circle.

Therefore, O'A' is equal to O'C.

This step can be explained using the definition of the center of a circle.

The center of a circle is the point equidistant from all points on the circle.

Therefore, C is on the circle and OA = OC.

This step can be explained using the reflexive property of equality. The reflexive property of equality states that a value is always equal to itself. Therefore, OC = O'C.

This step can be explained using the law of excluded middle. The law of excluded middle states that either a statement is true or its negation is true.

Therefore, either O lies on CO or it's opposite ray.Step i: This step can be explained using the definition of a contradiction. A contradiction is a statement that goes against a previously proven statement

. Therefore, if O lies on CO, then it contradicts the assumption that O = O'.Step j: This step can be explained using the definition of a ray. A ray is a line that extends infinitely in one direction. Therefore, if O lies on the opposite ray of CO, then it is not equal to O'.

This step can be explained using the definition of a contradiction. A contradiction is a statement that goes against a previously proven statement. Therefore, if O lies on the opposite ray of CO, then it contradicts the assumption that O = O'.

This step can be explained using the definition of a contradiction. A contradiction is a statement that goes against a previously proven statement. Therefore, if there is a contradiction, then the original assumption must be false.

Therefore, the proof can be concluded by stating that 0 = O' and that A and A' are on y, which implies that OA = OA' and O = O'.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The value of the x, y, and z for the given system of equations are; x =  -2/3, y = -1/2, and z = 1.

First, let us understand the equation:

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given the system of equations;

3x − 4y + z = 2                ...........equation 1

−9x + 12y − 3z = − 6       ...........equation 2

4x − 2y − z = -16             ...........equation 3

Add equation 1 to equation 3, we will get;

(3x − 4y + z ) + (4x − 2y − z ) =  2 -16

7x - 6y = -14  ...........equation 4

Multiply equation 3 by 3 and subtract from equation 2, we will get;

3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6

12x - 6y - 3z + 9x - 12y + 3z = 42

21x  - 18y = 42   ...........equation 5

Multiply equation 4 by 3 and add it to equation 4, we will get;

3(-3x + 3z) + (9x + 4z) = 5×3 - 2

-9x + 9z + 9x + 4z = 15 -2

13z = 13

z = 1

Put z = 1 in equation 5, we will get;

-3x + 3×1 = 5

-3x + 3 = 5

-3x = 5 - 3

x = -2/3

y = -1/2

Thus, the value of the x, y, and z for the given system of equations are; x =  -2/3, y = -1/2, and z = 1.

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Answer:

B

Step-by-step explanation:

Have a good dayyy :))

The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.

A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.

Given,

Cash prize = $100

Probability of winning the game = 0.7

Using binomial distribution,

P(4 ≤X≤ 6) = P( X = 4) + P( X = 5) + P( X = 6)

P( 4 ≤ X ≤ 6)

= 1/4(0.6)⁴(0.4)⁴ + 10/5 (0.6)⁵(0.4)⁵ + 10/6 (0.6)⁶(0.4)⁶

= 0.1115 + 0.2007 + 0.2508

= 0.5630

The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.

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Emily can ride her bike at a speed of 65 mph.

Let's use "x" to represent Emily's speed in mph.
We know that Kristen's speed is 8 mph faster, so her speed would be x + 8 mph.

We also know that Emily takes one hour longer than Kristen to travel 58.5 miles. So we can set up an equation:
\(\frac{58.5}{x}  = \frac{58.5}{x+8} +1\)

This equation represents the fact that the time it takes for Emily to travel 58.5 miles is one hour more than the time it takes for Kristen to travel the same distance.

Now, let's solve for x:
Multiplying both sides by x(x+8), we get:
\(58.5(x+8) = 58.5x + x(x+8)\)
\(58.5x + 468 = 58.5x + x^2 + 8x\)

Simplifying, we get:
\(x^2 + 8x - 468 = 0\)

Now we can use the quadratic formula:
\(x = \frac{(-8 ± \sqrt{8^{2} - 4(1)(-468) }}{2(1)}\)
\(x = \frac{(-8±\sqrt{18976)}}{2}\)
\(x = \frac{(-8±132)}{2}\)
x = -73 or x = 65

Since Emily's speed can't be negative, we can discard the negative solution. Therefore, Emily can ride her bike at a speed of 65 mph.

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Answer:

option C

Step-by-step explanation:

\(5 = \frac{4}{3}(6y + 9)\\\\5 = \frac{4\times6y}{3} +\frac{4 \times 9}{3}\\\\5= 8y + 12\)

Answer:

B: 2 2/3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Funny, because i'm learning about this right now. The best way to solve this is to imagine it in real life. Imagine having 2/3 of a cup of sugar to make 1/4 of a cake. To make a whole cake, you would need to multiply 1/4 times 4, to get 1 sheet cake. You have to do the same thing with the cups of sugar: 2/3 times 4, which would get you 2 2/3 cups, which is B. Please correct me if I am wrong, everybody makes mistakes.

Answer:

The answer is 30.

Step-by-step explanation:

The given expression is :

3a+3b

Put a = 6 and b = 4 in the above expression.

3a+3b = 3(6) + 3(4)

= 18+12

= 30

Now put a = 4 and b = 6 in the above expression.

3a+3b = 3(4) + 3(6)

= 12+18

= 30

Hence, the answer in both case is same i.e. 30.

Answer:

\(log7\)

Step-by-step explanation:

when adding logs, apply the log rule: \(\log _a\left(x\right)+\log _a\left(y\right)=\log _a\left(xy\right)\)

∴  \(\log\left(\frac{14}{3}\right)+\log\left(\frac{11}{5}\right)=\log\left(\frac{14}{3}\cdot \frac{11}{5}\right)\)

when subtracting logs, apply the log rule: \(\log _a\left(x\right)\:-\:\log _a\left(y\right)=\log _a\left(\frac{x}{y}\right)\)

\(\log\left(\frac{14}{3}\cdot \frac{11}{5}\right)-\log\left(\frac{22}{15}\right)=\log\left(\frac{\frac{14}{3}\cdot \frac{11}{5}}{\frac{22}{15}}\right)\\\\=\log\left(7\right)\)

Answer:

log 7

Step-by-step explanation:

Adding the first values :

Applied Rule : log a + log b = log(ab)

⇒ log (14/3) + log (11/5)

⇒ log (14/3 × 11/5)

⇒ log (154/15)

Subtracting the second values :

Applied Rule : log a - log b = log(a/b)

⇒ log (154/15 ÷ 22/15)

⇒ log (154 ÷ 22)

⇒ log 7

The income effect resulting from the change in the price of x1 is approximately 17.14. This means that, due to the price increase of x1, the consumer's purchasing power has decreased by 17.14 units.

To determine the income effect resulting from the change in the price of good x1 (from P1 to P1'), we need to calculate the difference in the consumer's purchasing power before and after the price change.

Calculate the consumer's original budget allocation:

Using the original prices P1 = 15, P2 = 30, and the original income I = 2513, we can substitute these values into the given equations for x1 and x2:

x1 = (21/7P1) = (21/7 * 15) = 45

x2 = (51/7P2) = (51/7 * 30) = 219

So, the original budget allocation is x1 = 45 and x2 = 219.

Calculate the new budget allocation:

With the new price of P1' = 65, we can substitute it into the equation for x1:

x1' = (21/7P1') = (21/7 * 65) = 195/7 ≈ 27.86

Since the price of x1 has changed, we need to recalculate the quantity of x2. However, we don't have enough information about the relationship between x1 and x2 to determine the exact new quantity of x2.

Calculate the difference in purchasing power:

To calculate the income effect, we need to compare the consumer's purchasing power before and after the price change. Since the price of x1 has increased, the consumer can afford to buy less of x1. The income effect measures the change in purchasing power as a result of the price change.

Difference in purchasing power = Original budget allocation of x1 - New budget allocation of x1

= x1 - x1'

= 45 - (195/7)

= (315 - 195)/7

= 120/7 ≈ 17.14

The income effect resulting from the change in the price of x1 is approximately 17.14. This means that, due to the price increase of x1, the consumer's purchasing power has decreased by 17.14 units.

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The number of days it would take for a news story to reach 1,500,000 shares include the following: B. 6 days.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

Based on the information provided above, the number of shares this news story can be modeled by the following exponential function;

\(y = 5(7)^x\\\\1500000=5(7)^x\\\\300000=(7)^x\)

By taking the natural log (ln) of both sides of the equation, we have:

Time, x = 6.4 ≈ 6 days.

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1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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The value of x for the given algebraic expression will be 9.

A mathematical expression that includes variables, constants, and algebraic operations (addition, subtraction, etc.) is known as an algebraic expression. Terms are used to construct expressions.

For instance, the formula for a rectangle's area (A) can be written as (l * b), where 'l' stands for the rectangle's length and 'b' for its width.  It can be represented as

A = l*b

Given algebraic expression is

\(\frac{x}{15} = \frac{12}{20}\)

Cross multiplying terms,

20*x = 15*12

Then, value of x will be

x= \(\frac{15*12}{20}\)

x= 9

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5 : 3  is the ratio of cooking times for the rice to pasta .

What does a math ratio mean?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.

                                    You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Rice takes 20 minutes to cook

pasta takes 12

the ratio of cooking times for the rice to pasta = 20  :  12

                                                                            = 5 : 3

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